I'm a recent Ph.D. graduate from the Institute of Applied Mathematics and the Department of Mathematics at the University of British Columbia. My primary research interests are stochastic dynamical systems and the associated modelling problems and techniques. Please read my CV, Research Statement, and Teaching Statement to learn more.

I am also a contributor to the UBC Math Educational Resources wiki which offers solutions to past math exams as well as instructional content. This project has been incredibly rewarding for me, not to mention loads of fun!

You can contact me via email: will.thompson@zoho.com.

**W. F. Thompson**, R. Kuske, and A. Monahan. Reduced α-stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noise.*Submitted. Preprint on arXiv.org*, May 2017.**W. F. Thompson**, R. Kuske, and A. Monahan. Stochastic averaging of systems with multiple time scales forced with α-stable noise.*SIAM Multi. Model. Simul.*, 13(4), 1194–1223, Oct. 2015.-
**W. F. Thompson**, A. Monahan, and D. Crommelin. Parametric estimation of the stochastic dynamics of sea surface winds.*AMS Jour. Atmos. Sci.*, 71(9), 3465-3483, Sep. 2014. **W. F. Thompson**, R. Kuske, and Y.-X. Li. Stochastic phase dynamics of noise driven synchronization of two conditional coherent oscillators.*DCDS-A*, 32(8), 2971-2995, Aug. 2012.- A. G. Fowler,
**W. F. Thompson**, Z. Yan, A. M. Stephens, B. L. T. Plourde, and F. K. Wilhelm. Long-range coupling and scalable architecture for superconducting flux qubits.*Can. Jour. of Phys.*, 86(4), 533-540, 2008.

One of the most basic stochastic processes that can be modelled by a SDE is the Ornstein-Uhlenbeck process, $x_{t}$, which satisfies the following SDE: $$dx_{t} = -\mu\,x_{t}\,dt + \sigma\,dW_{t}, \quad \mu > 0, \quad t \geq 0.$$ The term $dW_{t}$ represents a Gaussian white noise forcing, which essentially means that, over a short time interval $[t_{1},t_{2}]$, the trajectory of the system is perturbed by a normal random variable with mean zero and variance $|\,t_{2} - t_{1}\,|$. (Under construction...)

The essential question was ``Given a finite number of sensors that can be placed on (or in) the wall of an industrial smelter, what arrangement of the sensors minimizes the uncertainty in the wall shape profile?''. The results of our ten-day endeavour are published on the IMAs website here.